I am currently working on a data assimilation project where we are utilizing the ADAO library within Python. While using the 3DVAR method for data assimilation, we have encountered some issues and are unsure how to improve the algorithm to resolve these problems. Our estimation values suddenly converge to the true values rather than gradually converging. We are unsure why this is happening and how to improve the algorithm to resolve this problem.
my test case is to estimate the coefficient A in the cosine function y=cos(Ax) using the 3DVAR (Three-Dimensional Variational) method for data assimilation, iterating over sequential observations, updating the background state, and refining the parameter estimate with each cycle.